Ray diagrams (lenses) problem. I need full explanations.

[dantenewton]

Ray diagrams (lenses) urgent problem. I need full explanations.

1. The question

An object of height 2cm is placed 15 cm from a thin converging lens of focal length 10cm.
Complete the paths of two rays on the figure to show their passage through the lens to the image formed.

2. The attempt

http://www.flickr.com/photos/56105561@N05/5427538657/

If I have drawn wrongly, please kindly pinpoint the mistakes and suggest your answers. Thank you so much and have a nice day!

 

[gneill]

The rays given in the figure are not the principle ray nor the central ray, and neither passes through the focus on the object side. It doesn't look like these rays will converge at an image.

Look at a https://sites.google.com/a/ggwo.org/ggca_science_lab/Home/physics/physics-light-and-optics/physics-lenses" .

 

[dantenewton]

Thank you gneill, but I want to clarify my doubts:

the thing is that one light ray travels downwards and the other upwards from the top extremity of the object to meet the convex lens. The website you suggested doesn't give a ray diagram that has a light ray traveling upwards from the object. Can you help me?

 

[gneill]

Thank you gneill, but I want to clarify my doubts:

the thing is that one light ray travels downwards and the other upwards from the top extremity of the object to meet the convex lens. The website you suggested doesn't give a ray diagram that has a light ray traveling upwards from the object.

That's right! They don't show your rays because, for a thin converging lens, they won't converge on the image; they are divergent rays that do not contribute to the formation of the image.

The rays that will define the extent of the image are:

1. The ray along the lens axis (which is not refracted as its angle of incidence with all surfaces of the lens is 90°);

2. The principle ray which travels horizontally from the head of the object to the lens and is refracted so that when it emerges it passes through the focus on the opposite side of the lens; and

3. The 'straight through' ray that goes from the top of the object straight through the center of the lens and out the other side -- the lens refractions cancel for this ray, so it doesn't deviate from a straight line.

Rays 2 and 3 converge at the head of the image (the image is inverted). Ray 1 defined the foot of the image.

 

[rwisz]

3. Explanation

First, let's understand the basics of ray diagrams for lenses. Ray diagrams are graphical representations that show how light rays pass through a lens and form an image. They are an important tool in understanding the behavior of light and how it interacts with lenses. In this problem, we are dealing with a thin converging lens, which means it is a convex lens with a focal point where parallel rays of light converge after passing through the lens.

Now, let's look at the given information. We have an object that is 2cm in height and is placed 15cm away from the lens. The lens itself has a focal length of 10cm. To complete the ray diagram, we need to draw two rays from the top and bottom of the object, passing through the lens, and determine where they converge to form the image.

The first ray we will draw is the one passing through the center of the lens. This is known as the principal axis. Since the lens is thin, we can assume that this ray will pass straight through the lens without bending. This ray will continue until it intersects the focal point, which is located 10cm from the lens on the principal axis. This intersection point will be our first point for the image.

The second ray we will draw is the one passing through the top of the object, parallel to the principal axis. This ray will pass through the lens and bend towards the focal point. The point where this ray intersects the first ray will be our second point for the image.

Now, we can draw a line connecting these two points to complete the image. The image formed is virtual, meaning it is formed by the extension of the light rays and cannot be projected onto a screen. It is also upright and reduced in size, as the object is placed further away from the lens than the focal point.

In summary, the two rays we drew, the one passing through the center of the lens and the one parallel to the principal axis, show the path of light as it passes through the lens and forms the image. This ray diagram can also be used to determine the characteristics of the image, such as its size, orientation, and position. It is an essential tool in understanding the behavior of light and how lenses work.